Statistics_Assignment-3.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "7b01a4a4",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import stats\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import seaborn as sns \n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "35e80126",
   "metadata": {},
   "outputs": [],
   "source": [
    "def expected_value(values, weights):\n",
    "    values = np.asarray(values)\n",
    "    weights = np.asarray(weights)\n",
    "    return (values * weights).sum() / weights.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "93a141e1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.09"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c_count = [1,4,3,5,6,2]\n",
    "ch_prob = [0.015,0.20,0.65,0.005,0.01,0.120]\n",
    "expected_value(c_count, ch_prob)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "a7d9046e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th>Points</th>\n",
       "      <th>Score</th>\n",
       "      <th>Weigh</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Mazda RX4</td>\n",
       "      <td>3.90</td>\n",
       "      <td>2.620</td>\n",
       "      <td>16.46</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Mazda RX4 Wag</td>\n",
       "      <td>3.90</td>\n",
       "      <td>2.875</td>\n",
       "      <td>17.02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Datsun 710</td>\n",
       "      <td>3.85</td>\n",
       "      <td>2.320</td>\n",
       "      <td>18.61</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Hornet 4 Drive</td>\n",
       "      <td>3.08</td>\n",
       "      <td>3.215</td>\n",
       "      <td>19.44</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Hornet Sportabout</td>\n",
       "      <td>3.15</td>\n",
       "      <td>3.440</td>\n",
       "      <td>17.02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Valiant</td>\n",
       "      <td>2.76</td>\n",
       "      <td>3.460</td>\n",
       "      <td>20.22</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Duster 360</td>\n",
       "      <td>3.21</td>\n",
       "      <td>3.570</td>\n",
       "      <td>15.84</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Merc 240D</td>\n",
       "      <td>3.69</td>\n",
       "      <td>3.190</td>\n",
       "      <td>20.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Merc 230</td>\n",
       "      <td>3.92</td>\n",
       "      <td>3.150</td>\n",
       "      <td>22.90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>Merc 280</td>\n",
       "      <td>3.92</td>\n",
       "      <td>3.440</td>\n",
       "      <td>18.30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>Merc 280C</td>\n",
       "      <td>3.92</td>\n",
       "      <td>3.440</td>\n",
       "      <td>18.90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>Merc 450SE</td>\n",
       "      <td>3.07</td>\n",
       "      <td>4.070</td>\n",
       "      <td>17.40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>Merc 450SL</td>\n",
       "      <td>3.07</td>\n",
       "      <td>3.730</td>\n",
       "      <td>17.60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>Merc 450SLC</td>\n",
       "      <td>3.07</td>\n",
       "      <td>3.780</td>\n",
       "      <td>18.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>Cadillac Fleetwood</td>\n",
       "      <td>2.93</td>\n",
       "      <td>5.250</td>\n",
       "      <td>17.98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>Lincoln Continental</td>\n",
       "      <td>3.00</td>\n",
       "      <td>5.424</td>\n",
       "      <td>17.82</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>Chrysler Imperial</td>\n",
       "      <td>3.23</td>\n",
       "      <td>5.345</td>\n",
       "      <td>17.42</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>Fiat 128</td>\n",
       "      <td>4.08</td>\n",
       "      <td>2.200</td>\n",
       "      <td>19.47</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>Honda Civic</td>\n",
       "      <td>4.93</td>\n",
       "      <td>1.615</td>\n",
       "      <td>18.52</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>Toyota Corolla</td>\n",
       "      <td>4.22</td>\n",
       "      <td>1.835</td>\n",
       "      <td>19.90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>Toyota Corona</td>\n",
       "      <td>3.70</td>\n",
       "      <td>2.465</td>\n",
       "      <td>20.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>Dodge Challenger</td>\n",
       "      <td>2.76</td>\n",
       "      <td>3.520</td>\n",
       "      <td>16.87</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>AMC Javelin</td>\n",
       "      <td>3.15</td>\n",
       "      <td>3.435</td>\n",
       "      <td>17.30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>Camaro Z28</td>\n",
       "      <td>3.73</td>\n",
       "      <td>3.840</td>\n",
       "      <td>15.41</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>Pontiac Firebird</td>\n",
       "      <td>3.08</td>\n",
       "      <td>3.845</td>\n",
       "      <td>17.05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>Fiat X1-9</td>\n",
       "      <td>4.08</td>\n",
       "      <td>1.935</td>\n",
       "      <td>18.90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>Porsche 914-2</td>\n",
       "      <td>4.43</td>\n",
       "      <td>2.140</td>\n",
       "      <td>16.70</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>Lotus Europa</td>\n",
       "      <td>3.77</td>\n",
       "      <td>1.513</td>\n",
       "      <td>16.90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>Ford Pantera L</td>\n",
       "      <td>4.22</td>\n",
       "      <td>3.170</td>\n",
       "      <td>14.50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>Ferrari Dino</td>\n",
       "      <td>3.62</td>\n",
       "      <td>2.770</td>\n",
       "      <td>15.50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>Maserati Bora</td>\n",
       "      <td>3.54</td>\n",
       "      <td>3.570</td>\n",
       "      <td>14.60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>Volvo 142E</td>\n",
       "      <td>4.11</td>\n",
       "      <td>2.780</td>\n",
       "      <td>18.60</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             Unnamed: 0  Points  Score  Weigh\n",
       "0             Mazda RX4    3.90  2.620  16.46\n",
       "1         Mazda RX4 Wag    3.90  2.875  17.02\n",
       "2            Datsun 710    3.85  2.320  18.61\n",
       "3        Hornet 4 Drive    3.08  3.215  19.44\n",
       "4     Hornet Sportabout    3.15  3.440  17.02\n",
       "5               Valiant    2.76  3.460  20.22\n",
       "6            Duster 360    3.21  3.570  15.84\n",
       "7             Merc 240D    3.69  3.190  20.00\n",
       "8              Merc 230    3.92  3.150  22.90\n",
       "9              Merc 280    3.92  3.440  18.30\n",
       "10            Merc 280C    3.92  3.440  18.90\n",
       "11           Merc 450SE    3.07  4.070  17.40\n",
       "12           Merc 450SL    3.07  3.730  17.60\n",
       "13          Merc 450SLC    3.07  3.780  18.00\n",
       "14   Cadillac Fleetwood    2.93  5.250  17.98\n",
       "15  Lincoln Continental    3.00  5.424  17.82\n",
       "16    Chrysler Imperial    3.23  5.345  17.42\n",
       "17             Fiat 128    4.08  2.200  19.47\n",
       "18          Honda Civic    4.93  1.615  18.52\n",
       "19       Toyota Corolla    4.22  1.835  19.90\n",
       "20        Toyota Corona    3.70  2.465  20.01\n",
       "21     Dodge Challenger    2.76  3.520  16.87\n",
       "22          AMC Javelin    3.15  3.435  17.30\n",
       "23           Camaro Z28    3.73  3.840  15.41\n",
       "24     Pontiac Firebird    3.08  3.845  17.05\n",
       "25            Fiat X1-9    4.08  1.935  18.90\n",
       "26        Porsche 914-2    4.43  2.140  16.70\n",
       "27         Lotus Europa    3.77  1.513  16.90\n",
       "28       Ford Pantera L    4.22  3.170  14.50\n",
       "29         Ferrari Dino    3.62  2.770  15.50\n",
       "30        Maserati Bora    3.54  3.570  14.60\n",
       "31           Volvo 142E    4.11  2.780  18.60"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv('Carsq.csv')\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "657e009b",
   "metadata": {},
   "source": [
    "### Calculation for points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "f40c0f7b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.5965625000000006"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['Points'].mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "77e9b340",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.6950000000000003"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['Points'].median()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "dff7a65b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    3.07\n",
       "1    3.92\n",
       "Name: Points, dtype: float64"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['Points'].mode()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "6b69f8f3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.28588135080645166"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['Points'].var()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "ab6e27b2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5346787360709716"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['Points'].std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "dc6c3f28",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.17"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Range = max(df['Points']) - min(df['Points'])\n",
    "Range"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ffc8e677",
   "metadata": {},
   "source": [
    "## Calculation for Score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "cf35f3ce",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.2172499999999995"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['Score'].mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "236faec5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.325"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['Score'].median()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "97a3d4f2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    3.44\n",
       "Name: Score, dtype: float64"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['Score'].mode()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "db363301",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9573789677419356"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['Score'].var()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "1e950b45",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9784574429896967"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['Score'].std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "7559e164",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.9110000000000005"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Range = max(df['Score']) - min(df['Score'])\n",
    "Range"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c329fc23",
   "metadata": {},
   "source": [
    "## Calculation for Weigh"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "4a856d51",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "17.848750000000003"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['Weigh'].mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "46af3824",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "17.71"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['Weigh'].median()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "4e1c706b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    17.02\n",
       "1    18.90\n",
       "Name: Weigh, dtype: float64"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['Weigh'].mode()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "54e4469f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.193166129032258"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['Weigh'].var()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "0488932b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.7869432360968431"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['Weigh'].std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "22fbda5a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8.399999999999999"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Range = max(df['Weigh']) - min(df['Weigh'])\n",
    "Range"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "04953b84",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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hR5UG56ePSlLjPDUkSY0zBJLUOEMgSY0zBJLUOEMgSY0zBJLUOEMgSY0zBJLUuP8Dk0t7na5ZGBwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#The means of both Points and Score are closer\n",
    "plt.boxplot(x = 'Points', data =df)\n",
    "plt.xlabel('Points')\n",
    "plt.ylabel('Density')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "19b6693a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.boxplot(x = 'Score', data= df)\n",
    "plt.xlabel('Scores')\n",
    "plt.ylabel('Density')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "fc0e0ba6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.boxplot(x= \"Weigh\", data = df)\n",
    "plt.xlabel('Weigh')\n",
    "plt.ylabel('Density')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "0b0f1d2c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "145.33333333333331"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "weigh = [108,110,123,134,135,145,167,187,199]\n",
    "probs = [1/9,1/9,1/9,1/9,1/9,1/9,1/9,1/9,1/9]\n",
    "expected_value(weigh, probs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "c3121da5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Index</th>\n",
       "      <th>speed</th>\n",
       "      <th>dist</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>7</td>\n",
       "      <td>22</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>8</td>\n",
       "      <td>16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>6</td>\n",
       "      <td>9</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>7</td>\n",
       "      <td>10</td>\n",
       "      <td>18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>8</td>\n",
       "      <td>10</td>\n",
       "      <td>26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>9</td>\n",
       "      <td>10</td>\n",
       "      <td>34</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>10</td>\n",
       "      <td>11</td>\n",
       "      <td>17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>11</td>\n",
       "      <td>11</td>\n",
       "      <td>28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>12</td>\n",
       "      <td>12</td>\n",
       "      <td>14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>13</td>\n",
       "      <td>12</td>\n",
       "      <td>20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>14</td>\n",
       "      <td>12</td>\n",
       "      <td>24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>15</td>\n",
       "      <td>12</td>\n",
       "      <td>28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>16</td>\n",
       "      <td>13</td>\n",
       "      <td>26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>17</td>\n",
       "      <td>13</td>\n",
       "      <td>34</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>18</td>\n",
       "      <td>13</td>\n",
       "      <td>34</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>19</td>\n",
       "      <td>13</td>\n",
       "      <td>46</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>20</td>\n",
       "      <td>14</td>\n",
       "      <td>26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>21</td>\n",
       "      <td>14</td>\n",
       "      <td>36</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>22</td>\n",
       "      <td>14</td>\n",
       "      <td>60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>23</td>\n",
       "      <td>14</td>\n",
       "      <td>80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>24</td>\n",
       "      <td>15</td>\n",
       "      <td>20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>25</td>\n",
       "      <td>15</td>\n",
       "      <td>26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>26</td>\n",
       "      <td>15</td>\n",
       "      <td>54</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>27</td>\n",
       "      <td>16</td>\n",
       "      <td>32</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>28</td>\n",
       "      <td>16</td>\n",
       "      <td>40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>29</td>\n",
       "      <td>17</td>\n",
       "      <td>32</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>30</td>\n",
       "      <td>17</td>\n",
       "      <td>40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>31</td>\n",
       "      <td>17</td>\n",
       "      <td>50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>32</td>\n",
       "      <td>18</td>\n",
       "      <td>42</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>33</td>\n",
       "      <td>18</td>\n",
       "      <td>56</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>34</td>\n",
       "      <td>18</td>\n",
       "      <td>76</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>35</td>\n",
       "      <td>18</td>\n",
       "      <td>84</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>36</td>\n",
       "      <td>19</td>\n",
       "      <td>36</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>37</td>\n",
       "      <td>19</td>\n",
       "      <td>46</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>38</td>\n",
       "      <td>19</td>\n",
       "      <td>68</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>39</td>\n",
       "      <td>20</td>\n",
       "      <td>32</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>40</td>\n",
       "      <td>20</td>\n",
       "      <td>48</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>41</td>\n",
       "      <td>20</td>\n",
       "      <td>52</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>42</td>\n",
       "      <td>20</td>\n",
       "      <td>56</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>43</td>\n",
       "      <td>20</td>\n",
       "      <td>64</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>44</td>\n",
       "      <td>22</td>\n",
       "      <td>66</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>45</td>\n",
       "      <td>23</td>\n",
       "      <td>54</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>46</td>\n",
       "      <td>24</td>\n",
       "      <td>70</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>47</td>\n",
       "      <td>24</td>\n",
       "      <td>92</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>48</td>\n",
       "      <td>24</td>\n",
       "      <td>93</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>49</td>\n",
       "      <td>24</td>\n",
       "      <td>120</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>50</td>\n",
       "      <td>25</td>\n",
       "      <td>85</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Index  speed  dist\n",
       "0       1      4     2\n",
       "1       2      4    10\n",
       "2       3      7     4\n",
       "3       4      7    22\n",
       "4       5      8    16\n",
       "5       6      9    10\n",
       "6       7     10    18\n",
       "7       8     10    26\n",
       "8       9     10    34\n",
       "9      10     11    17\n",
       "10     11     11    28\n",
       "11     12     12    14\n",
       "12     13     12    20\n",
       "13     14     12    24\n",
       "14     15     12    28\n",
       "15     16     13    26\n",
       "16     17     13    34\n",
       "17     18     13    34\n",
       "18     19     13    46\n",
       "19     20     14    26\n",
       "20     21     14    36\n",
       "21     22     14    60\n",
       "22     23     14    80\n",
       "23     24     15    20\n",
       "24     25     15    26\n",
       "25     26     15    54\n",
       "26     27     16    32\n",
       "27     28     16    40\n",
       "28     29     17    32\n",
       "29     30     17    40\n",
       "30     31     17    50\n",
       "31     32     18    42\n",
       "32     33     18    56\n",
       "33     34     18    76\n",
       "34     35     18    84\n",
       "35     36     19    36\n",
       "36     37     19    46\n",
       "37     38     19    68\n",
       "38     39     20    32\n",
       "39     40     20    48\n",
       "40     41     20    52\n",
       "41     42     20    56\n",
       "42     43     20    64\n",
       "43     44     22    66\n",
       "44     45     23    54\n",
       "45     46     24    70\n",
       "46     47     24    92\n",
       "47     48     24    93\n",
       "48     49     24   120\n",
       "49     50     25    85"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1= pd.read_csv('speed_distance.csv')\n",
    "df1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "1b39f479",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For cars speed Skewness value=  -0.12\n"
     ]
    }
   ],
   "source": [
    "#The skewness value is negative so it is slightly left skewed\n",
    "print('For cars speed Skewness value= ',np.round(df1['speed'].skew(),2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "511068c1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For cars speed Kurtosis value=  -0.51\n"
     ]
    }
   ],
   "source": [
    "#Negative Kurtosis indicates that the distribution is not peaked.\n",
    "print('For cars speed Kurtosis value= ',np.round(df1['speed'].kurt(),2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "2e4f2e55",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For cars dist Skewness value=  0.81\n"
     ]
    }
   ],
   "source": [
    "#The skewness value is positive so it is slightly right skewed\n",
    "print('For cars dist Skewness value= ',np.round(df1['dist'].skew(),2))      "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "471dfa50",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For cars dist Kurtosis value=  0.41\n"
     ]
    }
   ],
   "source": [
    "#Positive Kurtosis value indicates that the distribution is peaked\n",
    "print('For cars dist Kurtosis value= ',np.round(df1['dist'].kurt(),2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "2872e646",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th>SP</th>\n",
       "      <th>WT</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>104.185353</td>\n",
       "      <td>28.762059</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>105.461264</td>\n",
       "      <td>30.466833</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>105.461264</td>\n",
       "      <td>30.193597</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>113.461264</td>\n",
       "      <td>30.632114</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>104.461264</td>\n",
       "      <td>29.889149</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>76</th>\n",
       "      <td>77</td>\n",
       "      <td>169.598513</td>\n",
       "      <td>16.132947</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>77</th>\n",
       "      <td>78</td>\n",
       "      <td>150.576579</td>\n",
       "      <td>37.923113</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>78</th>\n",
       "      <td>79</td>\n",
       "      <td>151.598513</td>\n",
       "      <td>15.769625</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>79</th>\n",
       "      <td>80</td>\n",
       "      <td>167.944460</td>\n",
       "      <td>39.423099</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>80</th>\n",
       "      <td>81</td>\n",
       "      <td>139.840817</td>\n",
       "      <td>34.948615</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>81 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    Unnamed: 0          SP         WT\n",
       "0            1  104.185353  28.762059\n",
       "1            2  105.461264  30.466833\n",
       "2            3  105.461264  30.193597\n",
       "3            4  113.461264  30.632114\n",
       "4            5  104.461264  29.889149\n",
       "..         ...         ...        ...\n",
       "76          77  169.598513  16.132947\n",
       "77          78  150.576579  37.923113\n",
       "78          79  151.598513  15.769625\n",
       "79          80  167.944460  39.423099\n",
       "80          81  139.840817  34.948615\n",
       "\n",
       "[81 rows x 3 columns]"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df2 = pd.read_csv('sp_wt.csv')\n",
    "df2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "c59e776f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For SP Skewness=  1.61\n"
     ]
    }
   ],
   "source": [
    "#The skewness value is positive so it is right skewed\n",
    "print('For SP Skewness= ',np.round(df2['SP'].skew(),2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "cdb73f0a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For SP Kurtosis=  2.98\n"
     ]
    }
   ],
   "source": [
    "# Positive Kurtosis value indicates that the distribution is peaked \n",
    "print('For SP Kurtosis= ',np.round(df2['SP'].kurt(),2)) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "81ee6415",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For WT Skewness=  -0.61\n"
     ]
    }
   ],
   "source": [
    "#The skewness value is negative so it is slightly left skewed\n",
    "print('For WT Skewness= ',np.round(df2['WT'].skew(),2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "7398293d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For WT Kurtosis=  0.95\n"
     ]
    }
   ],
   "source": [
    "#Positive Kurtosis value indicates that the distribution is peaked \n",
    "print('For WT Kurtosis= ',np.round(df2['WT'].kurt(),2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "d3f31402",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(198.7376089443071, 201.2623910556929)"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Confidence Interval for 94%\n",
    "ci94 = stats.t.interval(0.94,1999,200,30/np.sqrt(2000))\n",
    "ci94"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "0556a879",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(198.6214037429732, 201.3785962570268)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Confidence Interval for 96%\n",
    "ci96 = stats.t.interval(0.96,1999,200,30/np.sqrt(2000))\n",
    "ci96"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "c31de1f9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(198.4381860483216, 201.5618139516784)"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Confidence Interval for 98%\n",
    "ci98 = stats.t.interval(0.98,1999,200,30/np.sqrt(2000))\n",
    "ci98"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "800e5388",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The confidence intervals for 94% is [198.74 201.26]\n"
     ]
    }
   ],
   "source": [
    "print('The confidence intervals for 94% is',np.round(ci94,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "0019cad2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The confidence intervals for 96% is [198.62 201.38]\n"
     ]
    }
   ],
   "source": [
    "print('The confidence intervals for 96% is',np.round(ci96,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "4e550305",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The confidence intervals for 98% is [198.44 201.56]\n"
     ]
    }
   ],
   "source": [
    "print('The confidence intervals for 98% is',np.round(ci98,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "98bb1e02",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Confidence interval: [9.71, 10.64]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy.stats import t\n",
    "\n",
    "# generate some data\n",
    "data = np.random.normal(loc=10, scale=2, size=50)\n",
    "\n",
    "# calculate the sample mean and standard deviation\n",
    "sample_mean = np.mean(data)\n",
    "sample_std = np.std(data, ddof=1)\n",
    "\n",
    "# set the confidence level and degrees of freedom\n",
    "conf_level = 0.95\n",
    "dof = len(data) - 1\n",
    "\n",
    "# calculate the critical value\n",
    "crit_val = t.ppf((1 + conf_level) / 2, dof)\n",
    "\n",
    "# calculate the confidence interval\n",
    "margin_of_error = crit_val * (sample_std / np.sqrt(len(data)))\n",
    "lower_bound = sample_mean - margin_of_error\n",
    "upper_bound = sample_mean + margin_of_error\n",
    "\n",
    "# print the results\n",
    "print(f\"Confidence interval: [{lower_bound:.2f}, {upper_bound:.2f}]\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "152e4780",
   "metadata": {},
   "outputs": [],
   "source": [
    "data = pd.Series([34,36,36,38,38,39,39,40,40,41,41,41,41,42,42,45,49,56])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "ff11110b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0     34\n",
       "1     36\n",
       "2     36\n",
       "3     38\n",
       "4     38\n",
       "5     39\n",
       "6     39\n",
       "7     40\n",
       "8     40\n",
       "9     41\n",
       "10    41\n",
       "11    41\n",
       "12    41\n",
       "13    42\n",
       "14    42\n",
       "15    45\n",
       "16    49\n",
       "17    56\n",
       "dtype: int64"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "335f3548",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "41.0"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean = data.mean()\n",
    "mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "854d3637",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "40.5"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "median = data.median()\n",
    "median"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "3031843d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "25.529411764705884"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "var = data.var()\n",
    "var"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "bc07e481",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.05266382858645"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sd = data.std()\n",
    "sd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "9406e9ab",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:ylabel='Density'>"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "sns.distplot(data)  #he marks are normally distributed and slightly right skewed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "25adf5e8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>HP</th>\n",
       "      <th>MPG</th>\n",
       "      <th>VOL</th>\n",
       "      <th>SP</th>\n",
       "      <th>WT</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>49</td>\n",
       "      <td>53.700681</td>\n",
       "      <td>89</td>\n",
       "      <td>104.185353</td>\n",
       "      <td>28.762059</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>55</td>\n",
       "      <td>50.013401</td>\n",
       "      <td>92</td>\n",
       "      <td>105.461264</td>\n",
       "      <td>30.466833</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>55</td>\n",
       "      <td>50.013401</td>\n",
       "      <td>92</td>\n",
       "      <td>105.461264</td>\n",
       "      <td>30.193597</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>70</td>\n",
       "      <td>45.696322</td>\n",
       "      <td>92</td>\n",
       "      <td>113.461264</td>\n",
       "      <td>30.632114</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>53</td>\n",
       "      <td>50.504232</td>\n",
       "      <td>92</td>\n",
       "      <td>104.461264</td>\n",
       "      <td>29.889149</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>76</th>\n",
       "      <td>322</td>\n",
       "      <td>36.900000</td>\n",
       "      <td>50</td>\n",
       "      <td>169.598513</td>\n",
       "      <td>16.132947</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>77</th>\n",
       "      <td>238</td>\n",
       "      <td>19.197888</td>\n",
       "      <td>115</td>\n",
       "      <td>150.576579</td>\n",
       "      <td>37.923113</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>78</th>\n",
       "      <td>263</td>\n",
       "      <td>34.000000</td>\n",
       "      <td>50</td>\n",
       "      <td>151.598513</td>\n",
       "      <td>15.769625</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>79</th>\n",
       "      <td>295</td>\n",
       "      <td>19.833733</td>\n",
       "      <td>119</td>\n",
       "      <td>167.944460</td>\n",
       "      <td>39.423099</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>80</th>\n",
       "      <td>236</td>\n",
       "      <td>12.101263</td>\n",
       "      <td>107</td>\n",
       "      <td>139.840817</td>\n",
       "      <td>34.948615</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>81 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     HP        MPG  VOL          SP         WT\n",
       "0    49  53.700681   89  104.185353  28.762059\n",
       "1    55  50.013401   92  105.461264  30.466833\n",
       "2    55  50.013401   92  105.461264  30.193597\n",
       "3    70  45.696322   92  113.461264  30.632114\n",
       "4    53  50.504232   92  104.461264  29.889149\n",
       "..  ...        ...  ...         ...        ...\n",
       "76  322  36.900000   50  169.598513  16.132947\n",
       "77  238  19.197888  115  150.576579  37.923113\n",
       "78  263  34.000000   50  151.598513  15.769625\n",
       "79  295  19.833733  119  167.944460  39.423099\n",
       "80  236  12.101263  107  139.840817  34.948615\n",
       "\n",
       "[81 rows x 5 columns]"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cars = pd.read_csv('Cars.csv')\n",
    "cars"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "81fd014e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.348"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#P(MPG>38)\n",
    "P1 = np.round(1-(stats.norm.cdf(38,cars['MPG'].mean(),cars['MPG'].std())),3)\n",
    "P1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "64ee5459",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.729"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#P(MPG<40)\n",
    "P2 = np.round(stats.norm.cdf(40,cars['MPG'].mean(),cars['MPG'].std()),3)\n",
    "P2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "7217b0b1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.04394946224848731"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prob1 = stats.norm.cdf(20,cars['HP'].mean(),cars['HP'].std())\n",
    "prob1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "df33f0eb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.05712377632115936"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prob2 = stats.norm.cdf(20,cars['MPG'].mean(),cars['MPG'].std())\n",
    "prob2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "5c6cb8e9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.013174314072672048"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prob1 - prob2   #something wrong here "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "e147e693",
   "metadata": {},
   "outputs": [],
   "source": [
    "cars=pd.read_csv('Cars.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "a8269622",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>HP</th>\n",
       "      <th>MPG</th>\n",
       "      <th>VOL</th>\n",
       "      <th>SP</th>\n",
       "      <th>WT</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>49</td>\n",
       "      <td>53.700681</td>\n",
       "      <td>89</td>\n",
       "      <td>104.185353</td>\n",
       "      <td>28.762059</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>55</td>\n",
       "      <td>50.013401</td>\n",
       "      <td>92</td>\n",
       "      <td>105.461264</td>\n",
       "      <td>30.466833</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>55</td>\n",
       "      <td>50.013401</td>\n",
       "      <td>92</td>\n",
       "      <td>105.461264</td>\n",
       "      <td>30.193597</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>70</td>\n",
       "      <td>45.696322</td>\n",
       "      <td>92</td>\n",
       "      <td>113.461264</td>\n",
       "      <td>30.632114</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>53</td>\n",
       "      <td>50.504232</td>\n",
       "      <td>92</td>\n",
       "      <td>104.461264</td>\n",
       "      <td>29.889149</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>76</th>\n",
       "      <td>322</td>\n",
       "      <td>36.900000</td>\n",
       "      <td>50</td>\n",
       "      <td>169.598513</td>\n",
       "      <td>16.132947</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>77</th>\n",
       "      <td>238</td>\n",
       "      <td>19.197888</td>\n",
       "      <td>115</td>\n",
       "      <td>150.576579</td>\n",
       "      <td>37.923113</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>78</th>\n",
       "      <td>263</td>\n",
       "      <td>34.000000</td>\n",
       "      <td>50</td>\n",
       "      <td>151.598513</td>\n",
       "      <td>15.769625</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>79</th>\n",
       "      <td>295</td>\n",
       "      <td>19.833733</td>\n",
       "      <td>119</td>\n",
       "      <td>167.944460</td>\n",
       "      <td>39.423099</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>80</th>\n",
       "      <td>236</td>\n",
       "      <td>12.101263</td>\n",
       "      <td>107</td>\n",
       "      <td>139.840817</td>\n",
       "      <td>34.948615</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>81 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     HP        MPG  VOL          SP         WT\n",
       "0    49  53.700681   89  104.185353  28.762059\n",
       "1    55  50.013401   92  105.461264  30.466833\n",
       "2    55  50.013401   92  105.461264  30.193597\n",
       "3    70  45.696322   92  113.461264  30.632114\n",
       "4    53  50.504232   92  104.461264  29.889149\n",
       "..  ...        ...  ...         ...        ...\n",
       "76  322  36.900000   50  169.598513  16.132947\n",
       "77  238  19.197888  115  150.576579  37.923113\n",
       "78  263  34.000000   50  151.598513  15.769625\n",
       "79  295  19.833733  119  167.944460  39.423099\n",
       "80  236  12.101263  107  139.840817  34.948615\n",
       "\n",
       "[81 rows x 5 columns]"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cars"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "0d5f709c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(cars['MPG']);        #MPG cars follow normal distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "667e5e18",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Waist</th>\n",
       "      <th>AT</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>74.75</td>\n",
       "      <td>25.72</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>72.60</td>\n",
       "      <td>25.89</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>81.80</td>\n",
       "      <td>42.60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>83.95</td>\n",
       "      <td>42.80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>74.65</td>\n",
       "      <td>29.84</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>104</th>\n",
       "      <td>100.10</td>\n",
       "      <td>124.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>105</th>\n",
       "      <td>93.30</td>\n",
       "      <td>62.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>106</th>\n",
       "      <td>101.80</td>\n",
       "      <td>133.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>107</th>\n",
       "      <td>107.90</td>\n",
       "      <td>208.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>108</th>\n",
       "      <td>108.50</td>\n",
       "      <td>208.00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>109 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      Waist      AT\n",
       "0     74.75   25.72\n",
       "1     72.60   25.89\n",
       "2     81.80   42.60\n",
       "3     83.95   42.80\n",
       "4     74.65   29.84\n",
       "..      ...     ...\n",
       "104  100.10  124.00\n",
       "105   93.30   62.20\n",
       "106  101.80  133.00\n",
       "107  107.90  208.00\n",
       "108  108.50  208.00\n",
       "\n",
       "[109 rows x 2 columns]"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df3 = pd.read_csv('wc_att.csv')\n",
    "df3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "088335aa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(df3['Waist']);   #it is not normal distributi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "5af6c04b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(df3['AT']);        #it is not normal distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "7e3ebb2e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Z score for 90% confidence interval is [-1.645  1.645]\n"
     ]
    }
   ],
   "source": [
    "print('Z score for 90% confidence interval is',np.round(stats.norm.interval(0.90),3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "031895f4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Z score for 94% confidence interval is [-1.881  1.881]\n"
     ]
    }
   ],
   "source": [
    "print('Z score for 94% confidence interval is',np.round(stats.norm.interval(0.94),3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "9b1e727d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Z score for 90% confidence interval is [-0.842  0.842]\n"
     ]
    }
   ],
   "source": [
    "print('Z score for 90% confidence interval is',np.round(stats.norm.interval(0.60),3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "740c3828",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "T score for 95% confidence interval is [-2.064  2.064]\n"
     ]
    }
   ],
   "source": [
    "print('T score for 95% confidence interval is',np.round(stats.t.interval(0.95,24),3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "8e3cd10b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "T score for 96% confidence interval is [-2.172  2.172]\n"
     ]
    }
   ],
   "source": [
    "print('T score for 96% confidence interval is',np.round(stats.t.interval(0.96,24),3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "738189dc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "T score for 99% confidence interval is [-2.797  2.797]\n"
     ]
    }
   ],
   "source": [
    "print('T score for 99% confidence interval is',np.round(stats.t.interval(0.99,24),3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "3a486815",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.471"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t = np.round((260-270)/(90/np.sqrt(18)),3)\n",
    "t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "a6933ad3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability that bulbs have an average life of no more than 260 days is 0.32\n"
     ]
    }
   ],
   "source": [
    "print('The probability that bulbs have an average life of no more than 260 days is',np.round(stats.t.cdf(-0.471,17),2))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}